Abstract: Making use of Murakami's classification of outer involutions in a Lie algebra
and following the Morse-theoretic approach to harmonic two-spheres in Lie
groups introduced by Burstall and Guest, we obtain a new classification of
harmonic two-spheres in outer symmetric spaces and a Weierstrass-type
representation for such maps. Several examples of harmonic maps into classical
outer symmetric spaces are given in terms of meromorphic functions on $S^2$.